Animatronic Character problems.

So I am trying to make an animatronic-like character, a bit similiar to this:


But I have been running into problems. Please note I just newly started to use blender, and I just know a few things about modelling from the tutorials I have watched, still learning!
I was wondering how to make a part of an object wider?

As you can see that is pretty thin, I was wondering, how can I make the model’s circle parts wider?
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Bonus questions:
How do I put eye holes on a circle? I tried to do as the other tutorials said, they mainly used cubes and when I try to do what they did to my circle, it just messes up ;(

Bueller? Bueller? Anybody?